A055789 a(n) = binomial(n, round(sqrt(n))).

1, 1, 2, 3, 6, 10, 15, 35, 56, 84, 120, 165, 220, 715, 1001, 1365, 1820, 2380, 3060, 3876, 4845, 20349, 26334, 33649, 42504, 53130, 65780, 80730, 98280, 118755, 142506, 736281, 906192, 1107568, 1344904, 1623160, 1947792, 2324784, 2760681

Offset: 0

Author

Henry Bottomley, Jul 13 2000

Keywords

• easy
• nonn

Examples

			a(9) = C(9,3) = 9!/(3!*6!) = 84
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000194, A014062.

Programs

Magma

[Binomial(n, Round(Sqrt(n))): n in [0..40]]; // G. C. Greubel, Jan 25 2020

Maple

seq( binomial(n, round(sqrt(n))), n=0..40); # G. C. Greubel, Jan 25 2020

Mathematica

Table[Binomial[n, Round[Sqrt[n]]], {n,0,40}] (* G. C. Greubel, Jan 25 2020 *)

PARI

vector(40, n, binomial(n, round(sqrt(n))) ) \\ G. C. Greubel, Jan 25 2020

Python

from math import comb, isqrt
def A055789(n): return comb(n,(m:=isqrt(n))+ int((n-m*(m+1)<<2)>=1)) # Chai Wah Wu, Jul 29 2022

Sage

[binomial(n, round(sqrt(n))) for n in (0..40)] # G. C. Greubel, Jan 25 2020

Formula

a(n^2) = A014062(n).